To avoid the well-known drawbacks of the classical continuum damage theory
when localization occurs, an isotropic gradient-enchanced damage model is p
roposed in which the loading function ndt only depends on the damage value,
but also on its Laplacian. The initial boundary value problem obtained ado
pting this model is considered both in statics and in dynamics. In the dyna
mic context the finite-step problem is formulated according to a Newmark sc
heme; the constitutive law is integrated by the backward difference rule. A
n iterative procedure for the finite-step solution is discussed. Finite ele
ments space discretization is carried out in terms of generalized variables
on the basis of two variational principles pertinent to the two phases of
the iterative process. One- and two-dimensional numerical tests show the re
gularizing effect of the gradient term and the effectiveness of the propose
d discretization technique. Copyright (C) 1999 John Wiley & Sons, Ltd.